Testing basic phenomenological models of nuclear level density
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sting Basic Phenomenological Models of Nuclear Level Density M. I. Svirin Institute of Physics and Power Engineering, Obninsk, Kaluzhskaya oblast, 249033 Russia; e-mail: [email protected] Abstract—The problem of phenomenological description of nuclear level density is analyzed on the basis of testing the most important models: the Fermi gas and the generalized superfluid models and their modifications. Experimental data and numerical results for different characteristics related to the description of the level density as a function of excitation energy and nuclear composition are used in analysis. PACS number: 21.10.Ma DOI: 10.1134/S1063779606040010
INTRODUCTION Knowledge of the level density ρ(U, J) as a function of excitation energy U and angular momentum J of nuclei is necessary for multiple applications of the statistical theory of nuclear reactions; however, in spite of the high importance of this characteristic, its consistent description in a wide range of nuclei is still lacking. This situation is the consequence of both imperfection of theoretical models (consistent theoretical calculations of the level density are too complicated and cumbersome for a mass user) and difficulties of obtaining direct experimental information on the level density for excited nuclei. In the region in which the statistical description of ρ(U, J) is valid, this information is practically exhausted by the data on the observed neutron resonance density for the neutron binding energy U = Bn. As a result, phenomenological models and systematics have come into use; these are quite diverse and suitable for a wide range of requirements. However, their classification causes no difficulties: they are either empirical systematics, which most often are of no interest, or systematics based on theoretical models. In fact, there are two such models: the Fermi gas model (FGM) and the generalized superfluid model (GSFM). In FGM, starting with the classical work by Bethe [1], the excited nucleus is interpreted as a gas of noninteracting fermions. This assumption leads to a rather rough approximation in description of the statistical properties of real nuclei. For example, in order to describe the observed differences in ρ(U, J) for even– odd nuclei due to nucleon coupling in terms of FGM, it is necessary to introduce empirical corrections alien to the model itself. The effects of pair correlation of nucleons, one of the manifestations of which is differences of even–odd nuclei, are consistently taken into account by the superfluid model (SFM) of the nucleus [2, 3]. On the basis of this model, GSFM was developed [3, 4], which includes collective and shell effects. It may seem
that there is no dilemma in choosing between these two models. However, FGM, due to its simplicity and traditions, is very widespread and the scale of its application is incomparable with that of GSFM. This is partly justified: the two models are pretty close in their description of excitations above the critical energy of the phase transition from the superfluid state
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